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The present invention relates to methods for automated computerized clustering of data in any field of science and technology dealing with data processing.
Data clustering is a quest for order in chaos of data associated with objects under study and is meant to locate associative and genetic links between the objects. In data mining processes, clustering helps to discover the data distribution and patterns in the underlying data, thus increasing the practical and scientific value of a dataset. Most of the clustering techniques consist in data arrayal in such a way as to position the data points in the order of their compliance with certain criterion function of a search and then to join them in clusters based on scores of compliance with the search criterion function. Computer-implemented clustering methods work in an automated mode based on a pre-set criterion function of a search.
In most cases, a set of data associated with objects under study can be presented in the form of a similarity matrix which makes an original massif of data ready for comparative analysis and clustering based on calculated scores of similarity between objects, usually normalized within a range from 0 to 1 or 0 to 100%. Entries within a similarity matrix are then rearranged based on possibly highest proximity of quantitative characters, thus forming clusters and subclusters.
FIG. 1 shows a similarity matrix where S(x,y) is a score of similarity between objects x and y computed by any known technique. Even in cases when all n components of a matrix belong to a closely bound xe2x80x9cnaturalxe2x80x9d association of objects, such as, for example, a group of enterprises producing a certain type of goods by a certain type technology, or a group of taxonomically close microorganisms, or fish communities of different sections of a river, etc., a similarity matrix per se presents merely a tray of binary similarity cells (BS-cells) arranged according to man-made rules, while the true informational interrelation between the objects oftentimes remains unknown. In order to uncover the underlying infrastructure of informational relationships between the objects, a similarity matrix needs to be analyzed with the use of special techniques, in particular, clustering. A traditional approach to similarity matrix analysis implies that each of the 0.5(n2xe2x88x92n) binary similarity values is checked out and added to a pool of binary similarities of a certain group or subgroup.
However, it is easy to prove that the following is true for the matrix shown in FIG. 1:
S(A,B)≈1 S(A,C)/S(B,C)≈ . . . ≈S(A,n)/S(B,n),
i.e. that the 2nxe2x88x924 cells, too, contain the important and mostly non-additive information, in a non-linear form, on each of the binary similarity cells. Simply put, two similarity coefficients, S(A,C) and S(B,C), hide the information about S(A,B) which is not retrievable by the heretofore utilized methods for data mining. No generalized approach to solving the problem of extraction of hidden non-linear information has heretofore been proposed.
All heretofore existing methods for data clustering were based on processing of a similarity matrix in a stand-by state as, for example, statistical methods for BS processing in search for object correlations; or in its quasi-dynamic state when BS-cells are purposefully rearranged based on either simple criteria of obvious proximity, or according to more elaborate rules of data point sorting. In both types of a matrix processing, BS-cells remain intact or subjected to a parallel transfer to a different coordinate system.
The following is an example of data clustering based on analysis of a similarity matrix in its static state. In xe2x80x9cUsing Mean Similarity Dendrograms to Evaluate Classificationsxe2x80x9d (Van Sickle, 1997), similarity analysis is based on comparisons of mean similarities between objects within the same class to mean similarities between objects of different classes. The author analyzes similarities of a river""s various sites based on fish species presence/absence by using the data on the numbers of species common to the two sites and the numbers of species unique to each site, based on the data from three surveys conducted in 1944, 1983 and 1992 on fish assemblages along a 281-km stretch of the main-stem of Willamette River, Oreg. Earlier, other researchers (Hughes et al., 1987) hypothesized that four contiguous sections of the river""s 281-km stretch beginning at the river mouth, that could be distinguished based on channel depth and mapped channel gradients, would effectively correlate with the specifics of the river""s fish communities. The river""s four sections were identified as follows:
1) Section A, with 7 sites (a freshwater tidal section),
2) Section B, with 4 sites (a flat pool section),
3) Section C, with 4 sites (a section with low map gradient), and
4) Section D, with 4 sites (a shallow, upper section with higher map gradient).
FIG. 2A presents the similarity matrix of the data on fish assemblages sampled at Willamette river sites as given in the above referenced work by Van Sickle (1997). As is seen, it does not quite corroborate with the hypothesis of Hughes et al. (1987): the scores of similarity between different sites of the river""s Section D vary within the range of 47 to 67%; within Section C, from 62 to 82%; within Sections B and A, 50-75% and 27-86%, respectively. The ranges of variation of similarity between the sections do not yield any convincing information either: e.g. the score of similarity between Sections A and D varies within the range of 6.7% to 40.0%, i.e. changing almost six-fold.
Based on the above shown similarity matrix, the author derives a mean similarity matrix based on mean similarities within each river section and between the sections. As is seen from the mean similarity matrix derived by Van Sickle (1997) and shown in FIG. 3, the similarities between the river""s sections vary from 26 to 47%, while the similarities between individual sites within a section vary from 56 to 70%, thus showing that there is actually no remarkable difference between the lowest similarity score within clusters (56%) and the highest similarity score between different clusters (47%). Thus, the mean similarity-based analysis, as well as other mathematical statistics methods, which are used in data clustering merely out of xe2x80x9cscientific correctnessxe2x80x9d, has little, if any, value in understanding the data underlying the study. This is an example of xe2x80x9cpremeditated clusteringxe2x80x9d when mathematical statistics methods are applied to offer a proof of a certain assumption, or to substantiate an a priori designed clustering. From the following description of the present invention, it is seen that the method of this invention allows for finding perfect correlations in the above referenced data.
Another approach to clustering is based on analysis of a similarity matrix according to more sophisticated rules of data matching and sorting. For example, in the method described by Guha et al. in Programmed Medium For Clustering Large Databases (U.S. Pat. No. 6,092,072, Jul. 18, 2000), data points that may qualify for inclusion into a certain cluster are spotted in the chaos of data-in information by use of iterative procedures based on determining a total number of links between each cluster and every other cluster based upon an assigned pair of points to be neighbors if their similarity exceeds a certain threshold. Calculating a distance between representative points, then merging a pair of clusters having a closest pair of representative points, then calculating a mean of said representative points for said merged cluster, selecting a number of scattered data points from said representative points of said merged cluster and establishing a new set of representative points for said merged cluster by shrinking said number of scattered points toward the mean of the said cluster, and repeating those steps until a predetermined termination condition is met, clustering is performed along with eliminating outlier data points.
Unlike the above referenced purely statical approach when the positions of BS-cells do not change (Van Sickle, 1997), in the latter method, the BS-cells are continuously relocated as long as it takes a programmed medium to sort them out by agglomerating into a system with the lower informational entropy than that of an initial database.
There is a variety of other techniques for data clustering based on the heretofore accepted approach to data processing which can be described as xe2x80x9cuncooperative processingxe2x80x9d meaning that a similarity matrix is studied based on unchanging BS-cells (treated as sacred properties of experimentally obtained or compiled data) which are put together or apart at a discretion of a test system put into the basis of computer-implemented automated procedures. Alternatively, a cooperative processing of data involves a similarity matrix into a process that makes the matrix evolute and manifest, in the xe2x80x9cnaturalxe2x80x9d course of evolution, the genuine relationships between the objects under study. Speaking in terms of developmental biology, the evolution of a similarity matrix turns the bulk cells (BS-cells) into a body with differentiated organs (clusters, subclusters, sub-subclusters). There is a strong need for such a conceptually new method for data clustering based on cooperative processing of data which should provide for locating, extracting and consolidating the information contained in each BS-cell which indirectly represents each similarity value.
This invention provides a method, apparatus and algorithms for cooperative processing of a similarity matrix in the course of the matrix evolution resulting in discovery of the links of similarities and dissimilarities underlying in a non-obvious form in the matrix, hence the retrieval of additional unforeseen information about the components of the matrix.
The invention accomplishes the above and other objects and advantages by providing a method for unsupervised data clustering in the course of consecutive and irreversible transformations of a similarity matrix according to such algorithms that induce specific evolution of the matrix up to its asymptotic transition to an ultimately evolved state after which no further evolution is possible. Thus, the induced matrix evolution itself provides for clustering, however not according to deliberately imposed cluster boundaries, but reflecting the genuine relationship between similarities and differences of the components as revealed by the use of mechanism of evolution simulation.
The data-out represents a qualitatively new information extracted from the data-in, and the unforeseen relationships between objects under study can easily be uncovered by the use of the special techniques being an integral part of the method described in the present invention.
In order to trace the dynamics of a matrix up to the late stages of asymptotic transition towards the limit, the matrix is attenuated by means of introduction of a function of contrast. This allows for clear distinguishing of even such subtle changes of BS values as within a range from 0.99995 to 1.000.
Since the mechanism of a similarity matrix evolution provides for clustering in an auto-correlative mode, a complete hierarchical clusterization of the total of all objects under study can be performed in an automated mode as a uniform procedure, without setting forth any subjective conditions. Each of the clusters obtained upon the level-one division automatically undergoes further clustering by TDT-processing (transformation-division-transformation), and so on as long as there exist any detectable differences between the objects under analysis. The results of clustering can be presented in the form of dendrograms or trees pre-determined by and derived from the similarities and differences contained in the original matrix and unfolded during its evolution.
As a rule, unsupervised hierarchical clustering permits to find new unexpected information in the analyzed data. According to the second preferred embodiment of this invention, the extraction of heuristic information is efficiently enhanced by utilization of the technique of DBS-processing (analysis of dynamics of binary similarity) instead of TDT-processing step. To facilitate the process of information mining, all binary similarities displayed by a matrix during its evolution are recorded in the course of processing. DBS-processing technique permits to obtain a map of distribution of similarities between the matrix components (objects) which allows for evaluation of clusterization capacity of the matrix. A map showing a homogenous distribution of curves of dependence of BS on the number of evolution stages points to a low clusterization capacity of a matrix, and, alternatively, distinct gaps between the bundles of curves of BS dynamics correspond to hiatuses between individual clusters and indicate that the matrix has a high clustering capacity.
The advantage of DBS-processing is in its capability of fast and accurate locating of closest analogs of analyzed objects in the process of informational search.
A similarity matrix evoluting in accordance with the algorithm described of this invention is a self-learning system wherein the information accumulated in the process of transformation is conveyed to a newly derived successor-matrix which, in its turn, accumulates a new layer of information based on the associative capacity of a predecessor-matrix and conveys it to the next successor-matrix. This process is accompanied with self-occurring clustering, i.e. the transformation process itself attributes the produced information, finally and irreversibly, to the respective groups of objects. Such groups may either be individually subjected to further evolutionary transformation, or combined with related clusters produced by other matrices undergoing parallel transformation and enter a new cycle of transformation. This advantage of an evoluting matrix makes it usable as a constructive element of an artificial intelligence system.